﻿ 利用广义三角帽法评估GRACE/GRACE-FO反演流域陆地水储量变化的不确定性
 文章快速检索 高级检索
 大地测量与地球动力学  2023, Vol. 43 Issue (9): 957-962, 990  DOI: 10.14075/j.jgg.2023.09.014

### 引用本文

HUANG Jun, GU Yanchao, HUANG Feilong, et al. Uncertainties of Basin Terrestrial Water Storage Changes Inversed by GRCAE/GRACE-FO Using Generalized Three-Cornered Hat Method[J]. Journal of Geodesy and Geodynamics, 2023, 43(9): 957-962, 990.

### Foundation support

Young Scholars Development Fund of SWPU, No.201899010158; National Natural Science Foundation of China, No. 41931074; Natural Science Foundation of Sichuan Province, No. 2022NSFSC1113.

### Corresponding author

GU Yanchao, PhD, lecturer, majors in satellite gravity geodesy and its application, E-mail: yanchaogu@163.com.

### About the first author

HUANG Jun, postgraduate, majors in satellite gravity geodesy and its application, E-mail: hajun97@163.com.

### 文章历史

1. 西南石油大学土木工程与测绘学院，成都市新都大道8号，610500;
2. 武汉大学测绘学院，武汉市珞喻路129号，430079

1 广义三角帽法原理

 $\boldsymbol{X}_i=\boldsymbol{X}_{\text {true }}+\boldsymbol{e}_i, i=1,2, \cdots, N$ (1)

 $\begin{gathered} \boldsymbol{Y}_{i, N}=\boldsymbol{X}_i-\boldsymbol{X}_N=\boldsymbol{e}_i-\boldsymbol{e}_N, \\ i=1,2, \cdots, N-1 \end{gathered}$ (2)

 $\boldsymbol{S}=\boldsymbol{J} \cdot \boldsymbol{R} \cdot \boldsymbol{J}^{\mathrm{T}}$ (3)

 $\boldsymbol{J}_{N-1, N}=\left[\begin{array}{ccccc} 1 & 0 & \vdots & 0 & -1 \\ 0 & 1 & \vdots & 0 & -1 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \cdots & -1 \end{array}\right]$ (4)

 $\boldsymbol{G}\left(r_{1 N}, r_{2 N}, \cdots, r_{N N}\right)=\frac{1}{\boldsymbol{K}^2} \sum\limits_{i < j}^N r_{i j}^2$ (5)
 $\boldsymbol{H}\left(r_{1 N}, r_{2 N}, \cdots, r_{N N}\right)=-\frac{|\boldsymbol{R}|}{|\boldsymbol{S}| \cdot \boldsymbol{K}}<0$ (6)

 $\left\{\begin{array}{l} r_{1 N}^0=0, i 根据约束条件，通过最小化目标函数来获得N个自由参数。每组陆地水储量变化时间序列的不确定性通过标准偏差表示，即$\sigma_i=\sqrt{r_{i j}}\$

2 数据及研究区域 2.1 GRACE/GRACE-FO数据及后处理

2.2 研究区域

 大尺度流域： 1亚马孙 2扎伊尔 3密西西比 4鄂毕 5尼罗 6巴拉那 7勒拿 8阿穆尔 9尼日尔 10叶尼塞 11长江 12恒河-布拉马普特拉 13麦肯齐 14乍得湖 15伏尔加 16赞比亚 17萨斯喀彻温-尼尔森 18圣劳伦斯 19墨累-达令 20印度 21奥里诺科 22黄河 23育空 24湄公河 25朱巴-谢贝利 26多瑙河 27科雷马 28奥卡万戈 29科罗拉多 30哥伦比亚中尺度流域： 31圣弗朗西斯科 32奥兰治 33阿姆 34底格里斯-幼发拉底 35贝加尔湖 36第聂伯 37顿河 38珠江 39塞内加尔 40锡尔 41林波波 42伊洛瓦底 43西德维纳 44因迪吉尔卡 45戈达瓦里 46辽河 47乌拉尔 48弗雷泽 49鲁菲吉 50埃塞奎博小尺度流域： 51湄南河 52莱茵 53丘布特 54弗莱 55萨克拉门托 56卢瓦尔 57科罗拉多河 58库内纳 59杜罗 60讷尔默博 图 1 流域空间分布及气候类型 Fig. 1 Spatial distribution and climate type of basins
3 结果与分析 3.1 不同模型球谐系数相关性分析

 图 2 球谐系数模型在谱域上的相关系数 Fig. 2 Correlation coefficient of spherical harmonic coefficient models in the spectral domain
3.2 广义三角帽估计流域陆地水储量不确定性

 图 3 流域标准偏差空间分布及不同气候类型下的流域不确定性 Fig. 3 Spatial distribution of basin standard deviations and basin uncertainty under different climate types

 图 4 流域面积与流域陆地水储量变化不确定性 Fig. 4 Basin area and uncertainties of basin terrestrial water storage changes
3.3 典型流域的不确定性分析

 图 5 典型流域的陆地水储量变化时间序列 Fig. 5 Time series of terrestrial water storage changes in typical basins
4 结语

1) COST-G、CSR、JPL、ITSG和GFZ时变重力场模型反演全球60个流域的陆地水储量变化的平均不确定性分别是0.41 cm、0.63 cm、0.66 cm、0.81 cm和0.97 cm，组合模型COST-G反演结果的不确定性最低，GFZ模型精度最差。单一模型CSR、JPL、ITSG和GFZ具有较强的区域相关性。流域陆地水储量变化的不确定性与流域面积存在较强的相关性，而与气候类型的相关性较小。

2) 通常情况下，不同模型反演的陆地水储量变化具有较高的一致性，但当观测数据质量较差时，不同机构对数据处理的策略存在差异，从而导致不同模型反演的流域陆地水储量变化存在较大差异。虽然COST-G模型在全球尺度上具有较低的标准偏差，但若融合模型中的个别模型存在系统偏差则会导致其结果存在异常，进而严重影响COST-G模型反演的流域陆地水储量变化的不确定性。因此，在进行流域陆地水储量计算时，应开展多模型反演结果对比以选择合适的模型。

 [1] Sakumura C, Bettadpur S, Bruinsma S. Ensemble Prediction and Intercomparison Analysis of GRACE Time-Variable Gravity Field Models[J]. Geophysical Research Letters, 2014, 41(5): 1 389-1 397 DOI:10.1002/2013GL058632 (0) [2] 万祥禹, 游为, 王海波, 等. 基于多源数据分析维多利亚湖流域水储量变化[J]. 地球物理学报, 2021, 64(2): 441-454 (Wan Xiangyu, You Wei, Wang Haibo, et al. Terrestrial Water Storage Variations in Lake Victoria Basin from Multi-Source Data[J]. Chinese Journal of Geophysics, 2021, 64(2): 441-454) (0) [3] Swenson S, Yeh P J F, Wahr J, et al. A Comparison of Terrestrial Water Storage Variations from GRACE with in Situ Measurements from Illinois[J]. Geophysical Research Letters, 2006, 33(16) (0) [4] Ditmar P. How to Quantify the Accuracy of Mass Anomaly Time-Series Based on GRACE Data in the Absence of Knowledge about True Signal[J]. Journal of Geodesy, 2022, 96(8): 54 DOI:10.1007/s00190-022-01640-x (0) [5] Chen J L, Tapley B, Tamisiea M E, et al. Error Assessment of GRACE and GRACE Follow-on Mass Change[J]. Journal of Geophysical Research: Solid Earth, 2021, 126(9) (0) [6] Boergens E, Kvas A, Eicker A, et al. Uncertainties of GRACE-Based Terrestrial Water Storage Anomalies for Arbitrary Averaging Regions[J]. Journal of Geophysical Research: Solid Earth, 2022, 127(2) (0) [7] Ferreira V G, Montecino H D C, Yakubu C I, et al. Uncertainties of the Gravity Recovery and Climate Experiment Time-Variable Gravity-Field Solutions Based on Three-Cornered Hat Method[J]. Journal of Applied Remote Sensing, 2016, 10(1) (0) [8] 姚朝龙, 李琼, 罗志才, 等. 利用广义三角帽方法评估GRACE反演中国大陆地区水储量变化的不确定性[J]. 地球物理学报, 2019, 62(3): 883-897 (Yao Chaolong, Li Qiong, Luo Zhicai, et al. Uncertainties in GRACE-Derived Terrestrial Water Storage Changes over Chinese Mainland Based on a Generalized Three-Cornered Hat Method[J]. Chinese Journal of Geophysics, 2019, 62(3): 883-897) (0) [9] 郭飞霄, 孙中苗, 任飞龙, 等. GRACE RL06与RL05时变重力场模型数据初步比较分析[J]. 大地测量与地球动力学, 2020, 40(5): 546-550 (Guo Feixiao, Sun Zhongmiao, Ren Feilong, et al. Preliminary Comparative Analysis of GRACE RL06 and RL05 Time-Variable Gravity Models[J]. Journal of Geodesy and Geodynamics, 2020, 40(5): 546-550) (0) [10] Meyer U, Jean Y, Kvas A, et al. Combination of GRACE Monthly Gravity Fields on the Normal Equation Level[J]. Journal of Geodesy, 2019, 93(9): 1 645-1 658 DOI:10.1007/s00190-019-01274-6 (0) [11] Koot L, Viron O, Dehant V. Atmospheric Angular Momentum Time-Series: Characterization of Their Internal Noise and Creation of a Combined Series[J]. Journal of Geodesy, 2006, 79(12): 663-674 DOI:10.1007/s00190-005-0019-3 (0) [12] Galindo F J, Palacio J. Post-Processing ROA Data Clocks for Optimal Stability in the Ensemble Timescale[J]. Metrologia, 2003, 40(3): S237-S244 DOI:10.1088/0026-1394/40/3/301 (0) [13] Galindo F J, Palacio J. Estimating the Instabilities of N Correlated Clocks[C]. 31st Annual Precise Time and Time Interval Meeting, Dana Point, 1999 (0) [14] Tavella P, Premoli A. Estimating the Instabilities of N Clocks by Measuring Differences of Their Readings[J]. Metrologia, 1994, 30(5): 479-486 DOI:10.1088/0026-1394/30/5/003 (0) [15] Loomis B D, Rachlin K E, Luthcke S B. Improved Earth Oblateness Rate Reveals Increased Ice Sheet Losses and Mass-Driven Sea Level Rise[J]. Geophysical Research Letters, 2019, 46(12): 6 910-6 917 DOI:10.1029/2019GL082929 (0) [16] Loomis B D, Rachlin K E, Wiese D N, et al. Replacing GRACE/GRACE-FO C30 With Satellite Laser Ranging: Impacts on Antarctic Ice Sheet Mass Change[J]. Geophysical Research Letters, 2020, 47(3) (0) [17] Sun Y, Riva R, Ditmar P. Optimizing Estimates of Annual Variations and Trends in Geocenter Motion and J2 from a Combination of GRACE Data and Geophysical Models[J]. Journal of Geophysical Research: Solid Earth, 2016, 121(11): 8 352-8 370 DOI:10.1002/2016JB013073 (0) [18] Peltier W R, Argus D F, Drummond R. Comment on "An Assessment of the ICE-6G_C(VM5a) Glacial Isostatic Adjustment Model" by Purcell et al[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(2): 2 019-2 028 DOI:10.1002/2016JB013844 (0) [19] Wahr J, Molenaar M, Bryan F. Time Variability of the Earth's Gravity Field: Hydrological and Oceanic Effects and Their Possible Detection Using GRACE[J]. Journal of Geophysical Research: Solid Earth, 1998, 103(B12): 30 205-30 230 DOI:10.1029/98JB02844 (0) [20] Chen J L, Wilson C R, Tapley B D, et al. GRACE Detects Coseismic and Postseismic Deformation from the Sumatra-Andaman Earthquake[J]. Geophysical Research Letters, 2007, 34(13) (0)
Uncertainties of Basin Terrestrial Water Storage Changes Inversed by GRCAE/GRACE-FO Using Generalized Three-Cornered Hat Method
HUANG Jun1     GU Yanchao1     HUANG Feilong1     LI Qiong1     SU Yong1,2     XIONG Lingyan1
1. School of Civil Engineering and Geomatics, Southwest Petroleum University, 8 Xindu Road, Chengdu 610500, China;
2. School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
Abstract: Based on the generalized three-cornered hat method, we evaluate the uncertainties of global basin terrestrial water storage (TWS) changes calculated by five latest released GRACE/GRACE-FO time-varying gravity field models. Then, we investigate the effects of geographic location, climate type, and basin area on the uncertainties of basin TWS. The results show that: 1) The average uncertainties of basin-scale TWS changes for COST-G, CSR, JPL, ITSG, and GFZ models are 0.41 cm, 0.63 cm, 0.66 cm, 0.81 cm, and 0.97 cm, respectively. 2) Uncertainty in basin TWS changes is strongly correlated with geographic location and basin area, while climate type has little impact on the uncertainty. 3) There are large differences in the basin TWS changes from different solutions when observed data is poor.
Key words: GRACE/GRACE-FO; basin terrestrial water storage changes; generalized three-cornered hat; uncertainty